Problems in geometric drawing explained methods that could be used to produce geometric figures on paper when certain situational conditions existed that influenced the choice of the best or most convenient method to produce a desired or required figure. Geometric drawings were performed using several simple drawing tools including a measured straightedge for drawing right lines of any require length, a compass or dividers to both take distances and describe arcs of circles, and a protractor to measure the degrees of arcs of angles. While geometric drawings could not, in and of themselves, produce complete fortification drawings, they were employed in combination to achieve a fair degree of precision in laying out fortification plans and profiles on paper and were particularly useful in establishing proper defensive relationships between various elements of a fortification or line of fortifications.

During the middle period of the nineteenth century defensive relationships were essentially geometric relationships in which lines and angles were coordinated to allow different parts of a fortification or two independent fortifications to participate in each other's defense. It was a principle of fortification, for instance, that all angles of defense should be 90 degrees; that is, two lines of parapet arranged to defend each other should be perpendicular to each other. This principle transfers the question of adequate defensive relations to the realm of geometric drawing: to make sure that two lines are perpendicular one first has to know how to draw two lines that are perpendicular to each other. Another principle stated that the interior opening of salient angles should not be less than 60 degrees; again, it would be difficult to lay out a proper salient without knowing how to construct a 60 degree angle. Finding the capital of a salient angle would also be very difficult if one had no idea how to bisect an angle. In short, the art of fortification as it was practiced in the nineteenth century fundamentally begins with the ability to perform simple geometric drawings that establish the relationships among various elements of a fortification.

Given the importance of geometric drawing to the study of the art of fortification as it was practiced during the middle period of the nineteenth century a few simple samples of figure constructions have been provided below. Please click on the thumbnail image or title of each problem (or construction) to view complete instructions for performing the drawing on paper.